Non-equilibrium dynamics in Holography

In this thesis, we investigate aspects of non-equilibrium dynamics of strongly coupled field theories within holography. We establish a hydrodynamic description for anomalous quantum field theories subject to a strong external field for the first time in the literature. Within holography, we explicitly demonstrate which transport coefficients are non-zero due to the chiral anomaly and thus important for the transport. We show that the standard treatment of the hydrodynamics for spontaneously broken translational invariance is more subtle and has to be revised since the description is missing a novel thermodynamic coefficient. Within holographic massive gravity, we lay out a road map for extensions of hydrodynamics to momentum dissipation. Furthermore, we study the imprint of spontaneously broken translations beyond linear response theory in terms of periodically driven strongly coupled quantum field theories. Another important non-equilibrium scenario specially important for the understanding of our universe is quantum gravity in de-Sitter. Recently, the bold claim of the so-called swampland conjectures has attracted great interest since it banishes all stable theories of quantum gravity on de-Sitter with matter into swampland. Within the well-defined framework of the DS/dS correspondence, we set out to derive consistency conditions on the matter content in de-Sitter. Surprisingly, our proposed bound is violated by any reasonable form of matter. In our discussion, we find a novel one-parameter family of entangling surfaces which interpolates between the two solutions known so far. The last chapter is dedicated to solvable irrelevant deformations in quantum field theory -- the TT deformation. Within holography, we derive the entanglement entropies for generic subintervals on a sphere. We also resolve the confusion in the literature about a seeming mismatch between the holographic field theory results for the entanglement entropy in general dimensions

Real-time dynamics of axial charge and chiral magnetic current in a non-Abelian (expanding) plasma

Understanding axial charge dynamics driven by changes in Chern-Simons number densities is a key aspect in understanding the Chiral Magnetic Effect (CME) in heavy-ion collisions. Most phenomenological simulations assume that a large amount of axial charge is produced in the initial stages and that axial charge is conserved throughout the simulation. Within an (expanding) homogeneous holographic plasma, we investigate the real-time axial charge relaxation dynamics and their impact on the chiral magnetic current. Moreover, we discuss the real-time interplay of the non-abelian and the abelian chiral anomaly in the presence of a strong magnetic field. In the expanding plasma, the Chern-Simons diffusion rate and thus the axial charge relaxation rate are time dependent due to the decaying magnetic field. We quantify the changes in the late time falloffs and establish a horizon formula for the chiral magnetic current.Comment: 14+2 pages, 6+4 figure

Space-time dynamics of chiral magnetic currents in a hot non-Abelian plasma

The correlations of electric currents in hot non-Abelian plasma are responsible for the experimental manifestations of the chiral magnetic effect (CME) in heavy-ion collisions. We evaluate these correlations using holography, and show that they are driven by large-scale topological fluctuations. In a non-abelian plasma with chiral fermions, local axial charge can be generated either by topological fluctuations (creating domains with non-zero Chern-Simons number) or by thermal fluctuations. Within holography, we investigate the dynamical creation of the axial charge and isolate the imprint of the topological dynamics on the spatial correlations of electric current. In particular, we show that the spatial extent of the current correlation is quite large ($\sim 1\ {\rm fm}$) and grows with time, which is consistent with sphaleron-like dynamics. We provide numerical estimates for this spatial size that can be used as an input in phenomenological analyses.Comment: 9+1 pages, 6+3 figure

Holographic quenches and anomalous transport

We study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal "fast" quench response. Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes, by solving the (ODE) Laplace transformed equations. We investigate the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems. Finally, we highlight the existence of Landau level resonances in the electrical conductivity parallel to a magnetic field at finite frequency and show explicitly that these only appear in presence of the anomaly. We show that the existence of these resonances induces, among others, a long-lived AC electric current once the electric field is switched off.Comment: 34 pages, 10 figure

Critical and near-critical relaxation of holographic superfluids

We investigate the relaxation of holographic superfluids after quenches, when the end state is either tuned to be exactly at the critical point, or very close to it. By solving the bulk equations of motion numerically, we demonstrate that in the former case the system exhibits a power law falloff as well as an emergent discrete scale invariance. The later case is in the regime dominated by critical slowing down, and we show that there is an intermediate time-range before the onset of late time exponential falloff, where the system behaves similarly to the critical point with its power law falloff. We further postulate a phenomenological Gross-Pitaevskii-like equation that is able to make quantitative predictions for the behavior of the holographic superfluid after near-critical quenches. Intriguingly, all parameters of our phenomenological equation which describes the non-linear time evolution may be fixed with information from the static equilibrium solutions and linear response theory.Comment: 8+6 pages, 2+1 figure

Nonlinear Oscillatory Shear Tests in Viscoelastic Holography

We provide the first characterization of the nonlinear and time dependent rheologic response of viscoelastic bottom-up holographic models. More precisely, we perform oscillatory shear tests in holographic massive gravity theories with finite elastic response, focusing on the large amplitude oscillatory shear (LAOS) regime. The characterization of these systems is done using several techniques: (I) the Lissajous figures, (II) the Fourier analysis of the stress signal, (III) the Pipkin diagram and (IV) the dependence of the storage and loss moduli on the amplitude of the applied strain. We find substantial evidence for a strong strain stiffening mechanism, typical of hyper-elastic materials such as rubbers and complex polymers. This indicates that the holographic models considered are not a good description for rigid metals, where strain stiffening is not commonly observed. Additionally, a crossover between a viscoelastic liquid regime at small graviton mass (compared to the temperature scale), and a viscoelastic solid regime at large values is observed. Finally, we discuss the relevance of our results for soft matter and for the understanding of the widely used homogeneous holographic models with broken translations.Comment: v2: Matching the version published in PRL